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Vertex-degree sequences in complex networks: New characteristics and applications

Author

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  • Xiao, Wenjun
  • Lin, Longxin
  • Chen, Guanrong

Abstract

Many complex networks exhibit a scale-free vertex-degree distribution in a power-law form ck−γ, where k is the vertex-degree variable and c and γ are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to explore and analyze their vertex-degree sequences. We had shown before that, for a scale-free network of size N, if its vertex-degree sequence is k11, then the length l of the vertex-degree sequence is of order logN. In the present paper, we further study complex networks with an exponential vertex-degree distribution and prove that the same conclusion also holds. In addition, we verify our claim by showing many real-world examples. We finally discuss some applications of the new finding in various fields of science and technology.

Suggested Citation

  • Xiao, Wenjun & Lin, Longxin & Chen, Guanrong, 2015. "Vertex-degree sequences in complex networks: New characteristics and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 437-441.
    • Handle: RePEc:eee:phsmap:v:437:y:2015:i:c:p:437-441
    DOI: 10.1016/j.physa.2015.05.012
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